Rewrite as a simplified fraction. ${0.6\overline{61} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 661.6161...\\ 10x &= 6.6161...\end{align*}}$ Subtracting the two equations, we have: ${990x = 655}$ ${x = \dfrac{655}{990}} $ ${x = \dfrac{131}{198}} $